Two brothers, aged 15 and 13, and their female cousin, 15, were parasailing when a rope holding their parachute snapped, the Greek coastguard said.

The younger boy and his cousin died while the older boy is in a “serious condition with multiple injuries” in a hospital on the island.

The youngsters were being towed by a speedboat when the accident happened. The bodies were found on rocks near Lindos by members of the coastguard and the fire department who had been contacted by the person who controlled the boat, the Greek coastguard spokesman said.

“It is under investigation about how the rope was cut,” he added.

“The guy who controlled the speedboat and another person were arrested.”

A spokesman for the foreign office said: “We are supporting the family of two British people following their death in Rhodes, and are in contact with the Greek authorities.”